Question

Solve the following equation by finding the general solution:
1. 3cosx+1.8=0
2. 2tanx+7tanx+10=0

Answer 1

First rearrange the equation so that each isolates x:

FIRST EQUATION:
\[3 \cos x+1.8=0\]\[\cos x={1.8 \over 3}\]\[\cos x={3 \over 5}\]

SECOND EQUATION:
\[2 \tan x+7 \tan x+10=0\]\[9\tan x+10=0\]\[\tan x=-{10 \over 9}\]
Note that tanx=sinx/cosx, so we can express the second equation as:
\[{\sin x \over \cos x}=-{10 \over 9}\]
OR
\[\cos x = -{9 \sin x \over 10}\]
Now we can set the two equations equal to one another:
\[{3 \over 5}= -{9 \sin x \over 10}\]
By solving for x in this equation you should be able to get your answer!